All-solid lithium ion secondary batteries with the electrolyte including sintered ceramic material have high thermal stability compared s pith lithium secondary batteries in which nonaqueous electrolyte is used. However, an ail-solid lithium ion secondary battery having high capacity has yet to be put to practical use anywhere in the world. One of the reasons lies in the solid electrolyte itself. Three examples of the major characteristics required of solid electrolyte are high ion conductivity (electrical conductivity), high chemical stability, and a wide potential window. Among others, the garnet-type oxide ceramic material satisfies the high chemical stability and potential window requirements, and is therefore considered one of the most promising candidates for solid electrolyte (see, for example, J. Am. Ceram. Soc,. 2003, 86 (3), pp. 437-440, and Angew. Chem. Int. Ed., 2007, 46, 7778-7781).